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F3.4 · Explain major laws and principles of electricity and magnetism

Learn to explain major laws and principles of electricity and magnetism through clear examples and targeted practice.

Ontario Grade 11 Physics

Electricity and Magnetism

How charge moves, circuits behave, and electricity and magnetism are linked

A circuit is a complete path through which charge can move. Before using circuit rules, recall that a scalar has magnitude but no direction. Current, voltage, and resistance are scalars. Conventional current has a stated direction in a circuit diagram, even though its measured value is a scalar. In a metal wire, electrons move opposite to conventional current. For each circuit example, the system will be the named circuit or component. If a direction is needed, it will be defined before calculating.

What you will learn

Explain the roles of current, voltage, and resistance in a circuit.
Use Ohm’s law to predict current, voltage, or resistance for a component that follows the law.
Describe how current in a wire creates a magnetic field and how a changing magnetic field can produce current.
Apply basic series-circuit rules and check calculations using units, direction, and reasonableness.

1. Circuit quantities and Ohm’s law

Electric charge is a property of matter. It is measured in coulombs, symbol

\mathrm{C}

. Electric current describes how quickly charge passes a point. Current is measured in amperes, symbol

\mathrm{A}

. One ampere means one coulomb of charge passes a point each second. Conventional current is defined as the direction positive charge would move. In a metal wire, electrons move in the opposite direction.

Voltage, also called potential difference, describes energy transferred per unit charge between two points. It is measured in volts, symbol

\mathrm{V}

. A battery can provide a potential difference that drives current around a complete circuit. Resistance describes how much a component opposes current. It is measured in ohms, symbol

\Omega

Ohm’s law relates voltage, current, and resistance for a component when its physical conditions stay steady. It is useful for components that follow the law. It does not say that every component behaves the same way in all conditions. Rearranging the relationship lets us solve for any one of the three quantities. If voltage stays constant and resistance increases, current decreases.

A circuit diagram uses symbols to show components and their connections. In a single loop, the same current passes through each component. Choose a direction around the loop as positive before calculating. If a signed result is negative, the actual conventional current is opposite to the chosen direction.

V=IR

Current is measured in amperes, voltage in volts, and resistance in ohms.
Ohm’s law applies to components that follow it under steady physical conditions.
In a single-loop series circuit, current is the same through every component.

2. Rules for simple circuits

A series circuit has components connected one after another in a single path. Since there is only one route for charge to take, the current is the same through each component. The total resistance of series resistors is the sum of their resistances. Adding a resistor in series therefore increases total resistance.

A parallel circuit has branches that provide more than one path. The current from the source divides among the branches and combines again where branches join. For a basic parallel circuit connected across a source, each branch has the same potential difference as the source. These rules help explain why changing a component or adding a path can change the circuit’s current.

Charge is not used up as it passes through components. In a steady circuit, charge entering a junction each second equals charge leaving it each second. This is a conservation principle: charge is not created or destroyed in the circuit. Energy is transferred from the source to components, where it may be changed into other forms such as heat or light.

When explaining a circuit, identify whether it is series or parallel before applying a rule. Do not assume that the same current passes through all branches of a parallel circuit. Keep track of the given voltage and resistance, and use SI units in calculations.

R_{\mathrm{series}}=R_1+R_2+\cdots

Series components share one path, so the current is the same through each.
Series resistances add.
At a junction, total current entering equals total current leaving.

3. How electricity and magnetism are connected

A magnetic field is the region around a magnet or current-carrying wire where magnetic effects can be detected. Magnetic field diagrams use lines and arrows to show the field’s direction. Outside a bar magnet, the arrows are drawn from its north pole toward its south pole.

An electric current in a wire produces a magnetic field around the wire. Around a straight wire, the field pattern forms circles centered on the wire. Reversing the current reverses the magnetic-field direction. A coil is wire wound into loops. The magnetic fields from its loops combine, so a coil can produce a stronger field than a single straight section. A coil with an iron core is called an electromagnet. Its magnetic effect depends on the current and can be switched off by stopping the current.

The connection also works in the other direction. A changing magnetic field through a coil can produce a potential difference. If the coil is part of a closed circuit, this can produce a current. This process is called electromagnetic induction. For example, moving a magnet relative to a coil changes the magnetic field through the coil. If the magnet and coil remain still relative to each other, the field through the coil is not continually changing, so there is no continuing induced current.

A diagram or model can help show these relationships, but it is not itself measured evidence. A proposed demonstration or simulation can illustrate a predicted effect; it should not be described as a completed physical experiment unless measurements were actually made.

Current in a wire produces a magnetic field.
Reversing current reverses the magnetic-field direction.
A changing magnetic field through a coil can induce a potential difference and, in a closed circuit, current.

4. A careful method for circuit reasoning

First identify the physical system: for example, one resistor or a complete series circuit. List the known values and the unknown. If direction matters, state a positive conventional-current direction. Then choose the relevant circuit rule or relationship.

Substitute values with SI units shown. Keep units through the calculation. Report a sensible number of significant figures based on the values given. Current, voltage, and resistance are scalars, but a current direction can be stated in words relative to a circuit diagram or source terminal.

Finish by checking the units, direction, and size of the result. For Ohm’s law, volts divided by ohms must give amperes. At constant voltage, a larger resistance should give a smaller current. These checks help identify arithmetic or reasoning errors.

State the system, known values, unknown, and direction convention.
Use SI units and preserve them in substitutions.
Check units, significant figures, direction, and physical reasonableness.

Worked example

Current through one resistor

12.0\,\mathrm{V}

source is connected across a

4.0\,\Omega

resistor in a complete loop. Find the current and state its conventional direction.

Define the system and direction
The system is the source, resistor, and connecting wires in one loop. Choose conventional current from the source’s positive terminal, through the resistor, toward the negative terminal as positive. The unknown is current.
Choose the relationship
The resistor follows Ohm’s law under the stated circuit conditions. Rearrange the relationship to find current.
$I=\frac{V}{R}$
Substitute and calculate
Use the voltage and resistance in SI units. The positive result means current follows the chosen direction.
$I=\frac{12.0\,\mathrm{V}}{4.0\,\Omega}=3.0\,\mathrm{A}$

Answer: The current is

3.0\,\mathrm{A}

, flowing conventionally from the positive terminal through the resistor toward the negative terminal.

Check: A volt divided by an ohm is an ampere. The result is positive for the chosen direction. A

12.0\,\mathrm{V}

source across a

4.0\,\Omega

resistor gives a reasonable current of a few amperes.

Worked example

Voltage across a series resistor

2.0\,\Omega

resistor and a

4.0\,\Omega

resistor are in series with a

12.0\,\mathrm{V}

source. Find the current and the voltage across the

4.0\,\Omega

resistor.

Define the system and direction
The system is the single-loop series circuit. Choose conventional current from the positive terminal of the source as positive. The unknowns are circuit current and the voltage across the $4.0\,\Omega$ resistor.
Find total resistance
In series, resistances add. The source voltage is across the total series resistance.
$R_{\mathrm{total}}=2.0\,\Omega+4.0\,\Omega=6.0\,\Omega$
Find the circuit current
Apply Ohm’s law to the whole loop. A positive result means the current follows the chosen direction.
$I=\frac{12.0\,\mathrm{V}}{6.0\,\Omega}=2.0\,\mathrm{A}$
Find the resistor voltage
The same current passes through each series component. Use Ohm’s law for the $4.0\,\Omega$ resistor.
$V_2=(2.0\,\mathrm{A})(4.0\,\Omega)=8.0\,\mathrm{V}$

Answer: The circuit current is

2.0\,\mathrm{A}

. The potential difference across the

4.0\,\Omega

resistor is

8.0\,\mathrm{V}

Check: The current has units of amperes, and current times resistance gives volts. The other resistor has a

4.0\,\mathrm{V}

drop, so the two drops add to the

12.0\,\mathrm{V}

source. The values are consistent with the series-circuit rules.

Worked example

Comparing current as resistance changes

A component has a potential difference of

9.0\,\mathrm{V}

. Its resistance changes from

3.0\,\Omega

6.0\,\Omega

, while the voltage remains constant. Find both currents and compare them.

Define the system and direction
The system is the component. Choose conventional current from its higher-potential terminal to its lower-potential terminal as positive. The unknowns are the initial and final currents.
Calculate the initial current
Apply Ohm’s law using the initial resistance.
$I_1=\frac{9.0\,\mathrm{V}}{3.0\,\Omega}=3.0\,\mathrm{A}$
Calculate the final current
The voltage stays the same, so use the same relationship with the new resistance.
$I_2=\frac{9.0\,\mathrm{V}}{6.0\,\Omega}=1.5\,\mathrm{A}$

Answer: The current decreases from

3.0\,\mathrm{A}

1.5\,\mathrm{A}

. Doubling the resistance at constant voltage halves the current.

Check: Both voltage divided by resistance calculations give amperes. Both currents are positive for the chosen direction. The decrease is reasonable because current decreases when resistance increases at fixed voltage.

Common mistakes and how to avoid them

Treating conventional current as the direction electrons move in a metal wire.

Correction: Conventional current is defined as the direction positive charge would move. Electrons in a metal move in the opposite direction.

Assuming the current is the same in every branch of a parallel circuit.

Correction: Current divides among parallel branches. In a single-path series circuit, the current is the same through each component.

Saying charge is used up as it passes through a resistor or lamp.

Correction: Charge is conserved in a circuit. Components transfer energy from moving charge; they do not use up the charge.

Assuming a stationary magnet near a coil continually induces current.

Correction: Induction requires a changing magnetic field through the coil. A magnet and coil held still relative to each other do not continually change that field.

Using Ohm’s law as if every component behaves the same way in all conditions.

Correction: Ohm’s law applies to components that follow the relationship under the stated physical conditions.

Lesson summary

Ohm’s law relates voltage, current, and resistance for a component that follows the law.
In a series circuit, current is the same through each component and resistances add.
Charge is conserved: current entering a junction equals current leaving it.
Current produces a magnetic field; reversing current reverses the field direction.
A changing magnetic field through a coil can induce a potential difference and current in a closed circuit.
State the system and direction convention, use SI units, and check the result.

Check your understanding

Question 1

A component has a constant potential difference. Its resistance doubles. What happens to its current, if it follows Ohm’s law?

The current doubles.
The current becomes half as large.
The current stays the same.
The current must become zero.

Show answer and explanation

The current becomes half as large.

Ohm’s law gives current as voltage divided by resistance. With voltage fixed, doubling resistance halves current.

Question 2

In a single-loop series circuit, how does current through one resistor compare with current through another resistor?

It is the same through both.
It is always larger through the larger resistor.
It is always smaller through the larger resistor.
It becomes zero after the first resistor.

Show answer and explanation

It is the same through both.

A series circuit has one path for charge, so the same current passes through each component.

Question 3

Which change can produce an induced current in a closed coil?

Keeping a magnet and coil still relative to each other.
Changing the magnetic field through the coil.
Opening the circuit so there is no closed path.
Leaving the coil far from a stationary magnet.

Show answer and explanation

Changing the magnetic field through the coil.

A changing magnetic field through the coil can produce a potential difference and, when the circuit is closed, current.

Key terms

Electric charge: A property of matter measured in coulombs. Charge is not created or destroyed in an ordinary circuit process.
Electric current: The rate at which charge passes a point; measured in amperes.
Conventional current: The defined direction of current, matching the direction positive charge would move.
Voltage: Energy transferred per unit charge between two points; also called potential difference.
Resistance: A measure of how much a component opposes current.
Series circuit: A circuit with components connected along one path.
Parallel circuit: A circuit with branches that provide multiple paths.
Magnetic field: A region where a magnet or current-carrying wire can produce a magnetic effect.

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Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 11 Physics (SPH3U), expectation F3.4. It is a study resource, not an official curriculum publication.

Before publication, the draft is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability, and then requires administrator approval. Errors can still occur, so corrections are welcomed.

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